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i wasn't asking whether they could go into a tank with tropicals, i meant could a fantail goldfish be in a 10 gal tank by itself with no other fish of the same species or any other species and still be happy?

I am not sure whether there is any harm to a goldfish being in warmer water than they have been kept in historically. The issue that needs to be kept in mind is the rise in metabolic rate. This results in: 1-higher need for oxygen (they should have an air pump on the tank anyways), 2-more filtration (they need a lot anyways), and 3-more water changes (they definitely need a lot of that too). The water change schedule minimum is based on nitrate concentration, which needs to be no more than 20ppm. So although it is not really recommended, if they are already together and there are no issues then I would not worry about it.

As far as minimum tank size goes, the best guide I have seen is a minimum of a 20 gallon for one, and an additional 10 gallons for every additional goldfish. The other part is that they are schooling. So they are ideally in groups of at least 6. This puts a minimum sized school in a 65-75.